Boreholes are drilled deep into the earth for many applications such as carbon sequestration, geothermal production, and hydrocarbon exploration and production. Many different types of sensors may be used to perform measurements while a borehole is being drilled in an operation referred to as logging-while-drilling (LWD).
The standoff of an LWD sensor while one or more measurements are taken is a very important parameter. One of the important applications, for example, is to perform environmental corrections of the LWD sensor measurements, which are sensitive to the distance or standoff from the sensor to the formation. Usually, multiple ultrasonic transducers are mounted around the circumference of a bottom hole assembly (BHA) housing the LWD sensors. Each transducer measures the distance (i.e., standoff) from itself to the borehole wall in the direction of the acoustic waves.
The standoff values can also be used to give the geometry of the borehole. If the borehole is an ideal circle and the center of the downhole drilling assembly is at the center of the borehole, for example, the borehole radius can be calculated by adding the radius of the tool (from the center to the sensor) and the standoff (from the sensor to the borehole wall). In real drilling situations, however, the center of the downhole drilling unit usually moves laterally in the cross-section of the borehole due to drilling vibrations. The trajectory of its lateral movement cannot be known a priori. As a result, the geometry of the borehole cannot be obtained directly from the standoff measurements and the tool diameter. An algorithm is therefore necessary to remove the effect introduced by the lateral movement of the center of the drilling unit. Typically, traditional methods for this purpose do not handle arbitrary borehole geometry. For example, some existing algorithms assume the shape of arbitrary borehole geometry is elliptical even when it is not. It would be well received in the drilling industry if estimates of arbitrary borehole geometry could be improved.